An Easter Note - Cross, Crucification, Krish, Christ & Pre-Christian Beliefs

An Easter Note - Cross, Crucification, Krish, Christ & Pre-Christian Beliefs

Today is Easter & understanding the notes on Easter was of interest.

Googled and fell upon the following:

See link

See link

So much that, the Cross seems to be as revered as the Swastika and that the early Romans & Egyptians used the '+' sign for denoting the Sun - the God of Life.

Thus there exists a definitive adoptive link and therefore a continuity between the early customs and those adopted by the relatively new religions and that gives more authenticity & divinity to the ritual itself.

0 - x -- x0x -- x - 0

Zero divided by Zero

Zero divided by Zero

This might look very absurd but is interesting as a concept.  I believe that was sometime while I was in my 4th or 5th class, I asked my father about One divided by Zero (1/0).  He said that it cannot be determined.  He then asked a counter question of what was Zero divided by Zero (0/0).  I blinked as I didn't know nor could I deduce. He then said that it could be Zero, relating to the philosophy of the Upanishads that the Whole remains a Whole how many ever wholes you take out or don't. 

The Isaa-vaasya Upanishad says:

ऊँ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते ।

पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ।।

OM poornamadah poornamidam

poornaat poornamudachyate

poornasya poornamaadaaya

poornamevaavashishyate

That (God) is whole; this (world) is whole;

The whole manifested from the Whole.

From the Whole, even if whole is taken away,

what remains again is the Whole.

Thus Zero being considered a whole number in the Number System, just as its philosophical interpretation the above verse is, in terms of God/That as Infinity, the same applies to Zero too.  However, the young boy couldn't digest much of what he said then and it was left there.

When later on, I pursued my graduation in the Mathematics (1985-88), with the study of Real Numbers, Complex Numbers etc., the same problem returned for a better analysis again. 

During this time, I had few discussions with my classmates and with one of my Mathematics professors at St. Joseph's College, Calicut on my understanding of the concept of Zero divided by Zero. While one of my classmates thought there was merit, the professor rubbished though!. 

About that time, I had written an article in a magazine called 'Aarsha-naadam' combining the concept of Vedic Mathematics in arriving at the result of dividing Zero by Zero. (Though I had preserved the copy of the book for a long time, am unable to trace it now after many relocations in the many years that followed. My father used to subscribe to  copies of that bi-monthly magazine those days).

However, I will briefly explain the concept that I had tried to impress on the readers then.  

In the methodology of Vedic Mathematics, (Nikhilam sutra), in case of a division, instead of subtraction, addition is performed by 'Nikhilam' of the divisor, so as to equalize the multiplier to the quotient part of resultant (i.e. excluding the remainder).  (Nikhilam is defined as "nikhilam navatas-charamam dasatah" ie. difference all from 9, last from 10. This in effect becomes the tens complement).  The resultant will have two parts namely the quotient part and the remainder part;  the remainder part will have as many digits as there are in the divisor.  Initially, the dividend itself is considered as the resultant and the multiplier is assumed to be equal (or about) the quotient part of the resultant.  

To be more detail, let us say we want to divide 9 by 7.  For this, the dividend is 9, the divisor is 7.  Considering, the dividend itself as the initial resultant, reserving as many digits as there are in the divisor for the remainder, which is 1 (as the divisor 7 is single digit), we get the initial multiplier as 0 and initial remainder as 9 (assuming that the dividend is 09).  Taking Nikhilam of 7, we get 3 which is (10 - 7). Multiply this 3 by a suitable multiplier in this case 1 giving 1 x 3 = 3 and Add this product 3 to the dividend 9 to get 12.  Since the base of the nikhilam was 10, and the power of the base being 1, we partition the resultant into two parts; the last 1 digit forms the remainder part and the remaining forms the quotient part.  Partitioning the resultant 12 into two by removing the last 1 digit we have 1 in the quotient part and 2 in the remainder part.  Well that is exactly the answer provided that the remainder is not bigger than the value of the quotient in which case, the next higher multiplier is to be considered. This condition hasn't arisen here, since the quotient part of the resultant is 1 which happens to be equal to the multiplier, we can conclude that our quotient is 1 and remainder is 2. 

---

Eg: Divide 9 by 7:

		Resultant
		(quotient-part)	(remainder-part)
	divisor	dividend		multiplier
	7	0	9	0
Nikhilam  of divisor =	3		3	1
		12
(Note:- multiplier to be maintained equal to quotient always)		1	2
		quotient	remainder

In the above example, if we were to consider 0 as the quotient, then the remainder would have been 9 which is not allowed since the remainder cannot be greater than the divisor.  Hence the next number to be taken ie. 1.  Multiplying the multiplier 1 by the Nikhilam of 7 which is 3, we get 1 x 3 = 3 which is put below the dividend.  The sum gives 12 with 1 in the quotient part and 2 in the remainder part.  The number of digits in the remainder part is understood from the number of digits in the divisor (because the remainder has to be less than the divisor).  Thus the end result is that 9 divided by 7 gives 1 as quotient and 2 as remainder.

---

Eg: Divide 4536132 by 8996:-

		Resultant
		(quotient-part)	(remainder-part)
	divisor	dividend		multiplier
	8996	0453	6132	0453
Nikhilam  of divisor =	1004	000	0	0
		40	16	4
		5	020	5
			3012	3
multiplier not tallying:-		0499	0944	0045 / 0498
		000	0	0
		00	00	0
		4	016	4
			5020	5
multiplier not tallying:-		0503	6124	0004 / 0502
		000	0	0
		00	00	0
		0	000	0
			4016	4
multiplier not tallying:-		0504	0140	0002 / 0504
		000	0	0
		00	00	0
		0	000	0
0504 - 0502 = 2			2008	2
(Note:- multiplier to be maintained equal to quotient always)		0504	2148
		quotient	remainder

---

A non-detailed way of writing the above would be as follows:-

		Resultant
		(quotient-part)	(remainder-part)
	divisor	dividend		multiplier
	8996	0453	6132	0453
Nikhilam of divisor =	1004	40	16	4
		5	020	5
			3012	3
		4	016	4
			5020	5
			4016	4
multiplier not tallying:-		0504	0140	0002 / 0504
0504 - 0502 = 2			2008	2
(Note:- multiplier to be maintained equal to quotient always)		0504	2148
		quotient	remainder

---

Thus 4536132 divided by 8996 gives 504 as quotient and remainder 2148. 

Having understood the above division technique let us summarize the following rules:-
1. The number of digits of the remainder should be equal to the number of digits of the Nikhilam of the divisor. 
2. If the remainder is 0, then the divisor is fully divisible.  Otherwise, the remainder should be less than the divisor so that it ends up as a proper fraction.

3. The multiplier of the Nikhilam of the divisor should be equal to the quotient. 
   

Let us now try to divide 0 by 0 using this Vedic Mathematics method. 
The Nikhilam of 0 is expressed as a single digit below as 'T' indicating the value Ten.  Having taken T to represent 10, the arithmetic of T could be defined as:- 

1  x  T   =  T

 2  x  T  =  1T

  3  x  T  =  2T

  4  x  T  =  3T

.... 

....

 T  x  T  =  9T

		Resultant
		(quotient-part)	(remainder-part)
	divisor	dividend		multiplier
	0	0	0	0
Nikhilam  of divisor =	T		0
multiplier tallying:-		0	0	0 / 0
(Note:- multiplier to be maintained equal to quotient always)		0	0
		quotient	remainder

While the rules have been applied properly and the right answer has been obtained as quotient = 0 and remainder = 0,  for academic interest let us see, what would happen if the multiplier was taken as 1 instead of 0?

		Resultant
		(quotient-part)	(remainder-part)
	divisor	dividend		multiplier
	0	0	0	1
Nikhilam  of divisor =	T		T
multiplier not tallying:-		0	T	1 / 0
(Note:- multiplier to be maintained equal to quotient always)		0	T
		quotient (Erroneous)	remainder  (Erroneous)

Here we can see that it is not possible to have the multiplier equal to the quotient part as the quotient part is 0 while the multiplier part is 1.    Hence, it has to be concluded that the quotient for 0 divided by 0 is 0 and not any other number. 

Caution:-  However, there is a word of caution in this answer.  This is simple Arithmetic and not Mathematics.  In Arithmetic, I would hold that 0 divided by 0 = 0.  However in Mathematics, I would like to believe that it could be something else too.  

The reason for this is because, Arithmetic deals with absolute numbers.  Whereas Mathematics deals will approximate numbers as well.  Just as in physics, mathematics has for eg. in case of differentiation, say, 

                                 Limit    [Sin(A) /  A]   =   1

A --> 0

If A were to be substituted by 0, then Sin(A) would have been 0 and A itself is 0 which could have given [ Sin(A) / A ] =  [0 / 0]   = 0.   Whereas since we deal here with approximate 0 and not absolute 0,  we get the result 1. 

Therefore, what I would like to mention is that even though arithmetically,  0 / 0 = 0 in its absolute terms, mathematically, it cannot be considered so due to the fact that mathematics and physics consider numbers as approximates.  Another example to the same is the number  2.99999999999......  which in mathematics is equal to 3.  The number 3.00000000........000001  is also equal to 3 in mathematics.

x -  0 -  x -  0  -  x

Is God Personal or Impersonal

Is God Personal or Impersonal


Was going through an article on Personal God vis-a-vis Impersonal God and that kept me wondering whether God is personal or impersonal - if so at what level and state of our mind?

For that matter, I have many times wondered whether animals too have God!!  Is their God similar to ours? Do they have different religions and do they fight between each other to establish the supremacy of one God over the other - at least for their emotional satisfaction?  For that matter do animals have emotions at all?  Certain animals have been seen to show emotion at times!!

Sometime in 2007-08, when Orkut was very popular, I had once posted a small analogy about idol-worship to be more precise about the use of Linga (Shiva Linga) in worship.  Many posts recommended that Idol worship is not sanctioned in Vedas or Hinduism or any other religion.  To which I had commented in the following manner.

"Assume that you asked a mathematician to find out son's age if the son's age times the age of his nineteen year older mother, would give six hundred and sixty six. What would the mathematician do?.  He would most probably convert the question into something as follows:

   Let the unknown age of the son be x.
   Then, his mother's age would be (x + 19).
   Stated that   x ( x + 19) = 666
   ie.     x²  + 19x - 666 = 0
   ie.     (x + 37) (x - 18) = 0
   ie.   x = -37    or    x = 18
  Thus  the age of the son is 18 yrs."

The mathematician in the story could be any one of us in pursuit of God the unknown.  Inorder to find that God, (albeit it is not impossible to find the age of the son in the problem stated above without writing down anything, but by effectively utilizing faculties of the mind by good concentration and mediation, and with all its abstractness by perhaps a genius or one with good practice), an ordinary mathematician would just love to use the 'unknown variable', name it 'x' and try to solve the mystery.

Doesn't this analogy correspond to an Advaita/Vedantic philosopher pursuing an Impersonal God (Nir-Guna) in his capacity of possessing more intelligence with practice that he undertakes vis-a-vis a Dwaita-vaadi philosopher pursuing a God with Personal characteristics (Sa-Guna) conceived with a form that is Human or otherwise, or even a sound (viz. ॐ),  a story, a verse or a poem, a symbol (viz. Linga / Swastika, Cross etc.) or an Idol (viz. of Rama, Krishna, Durga, Mecca etc.).

While an abstract concentrated and intellectual effort is required in the former case by an intellectual mathematician, the latter gives a solution in more easily understandable, approachable and reachable way wherein each step can be verified anytime later, if required, for any errors or faults with scope for rectification wherever.  While in the former case, practice, intuition and experience is important, the latter requires dedication and devotion along with firm belief that the path is right, more so because it has already been tread and because it can be used and reused by anybody anytime (that methodology which is nowadays usually termed as 'scientific').

Thus the concept of Idol worship is to stay and should we say, that is a more easier and safer path than the abstract path which might not be easy enough for anyone with not-that sufficient mental faculties. 

I love to say anytime at such discussions that it is said that Adi-Shankaracharya the greatest Advaita-vaadi, knowing this fact very well, established temples throughout the length and breadth of India, installed idols of gods and goddesses for the comfort and upliftment of lesser souls and his invocations to Personal God-head viz. Krishna, Shiva, Lakshmi, Saraswati, Lalita etc. are filled with height of Devotion.  Alongside, it can be noted that Sri Ramakrishna Paramahamsa (Guru of Swami Vivekananda) was an ardent Idol worshiper with impeccable Bhakti / Devotion who later-on, also practiced Advaita-Vedantic style and concluded that the same goal was achieved following both the paths.

Thus, the answer is the same, while different people use different methods to arrive at it.  Just as the case of the genius and the mathematician would have solved the problem stated above.

Some Dvaita-vaadis however try to establish that God is but Personal and cannot be Impersonal at all. They like to tell us that God is benevolent, talks, shares & helps, etc. etc. and therefore should have a mind, a tongue, a hand, a heart etc.  The question that could be put across to such arguments is to try to find an analogy in a Computer.

A computer responds to questions and commands that we give.  Does it mean that it has a mind?  It talks to another computer in a LAN (Local Area Network) using a protocol like TCP/IP after making a handshake.  Does it mean that it has a hand for the hand-shake to happen?  It shares its files and folders with another computer and helps it get what it needs.  Does it mean that it has a 'heart'?

Thus it can also be understood that when the Upanishads or the Vedas speak of Brahman in terms of benevolence, talking, waving, etc., or having many hands, heads, intelligence etc., it does not mean that the God has a particular form.

The Upanishads proclaim that God does not have a likeliness to anything other that it; “न तस्य प्रतिमा अस्ति”. This means that none can be equal to or like God. Thus the 'x' in our equation is not equal to the answer itself, but is only a means to achieving the answer.  Therefore, idols or images could be tools to reach the ultimate. In other words, it makes sense to understand that Idol worship is also a form of worship that can give results just as any other.

Brahman cannot be likened to any other and therefore, it is unique - Advaita - that which is unlike another.

The Vedas say that it is not possible to even describe Brahman because, the moment we start to try to, we disqualify it of itself.

Being Nirguna, the Lord does not interfere in our daily lives - rather should not be doing so.  Imagine the Chairman of a large organization who interferes in each and everything that even the attender does?.  Will he be then doing the Chairman's job or the attenders' job?.  Therefore, the Chairman should ideally be concentrating on the policy matters and not even in the execution of the policy. This Policy is to be rather understood as 'Dharma' of the different jobs that are to be done by each and every one in the organization.  The hierarchy is defined and thanks to the intellectual and physical capabilities of each individual, he applies and is awarded the specific job that he is supposed to undertake inorder to contribute to the welfare of each and every one in the organization.  This is what is known as 'Varna' Dharma.

The Chairman has to be nirguna as he should not have any attributes attached to himself.  There could be a Director of Human Resources, a Director of Finance, a Director of Marketing, a Director of Operations or a Director of Information Technology who all have Gunas (Attributes); but not the Chairman (Guna-Ateeta).  This will ensure that there be no prejudice of any sort and that would improve confidence and belief in each of the many humans in the organization.

- 0 - x - 0 -